Oh yeah, me and
Warwolf sat down to discuss the 'plot hole' of the two fleets not meeting each other, and we came up with this, based on a
lot of assumptions.
Despite characters who haven't actually seen Danny's fleet claiming that Greyjoy fleet is the largest, that's physically impossible considering that Danny has to transport between 100,000-200,000 men. For the Mongolian invasion of Japan, the closest thing we have to something of this scale, the Mongols needed roughly 1000 ships for 50,000 men (900 for 40,000 to be more specific, but it's easier to work with fuller numbers). That's considering that a large chunk of the Mongolian navy was made up of riverboats and, to be blunt, crap. So theoretically Danny would need roughly 3000 ships, but since her ships appear to be more sea-worthy, we decided to say that 2500 would suffice. That means that her fleet is made up of 2500 ships and the Greyjoy fleet is made up of 1000 ships. Note that Greyjoy fleet might still be the largest battle fleet - Danny's fleet is largely supplemented by merchant ships.
Calculating the size of the strait between Dragonstone and the other bits is quite easy. The wall is about 300 miles. Someone out on Roddit already said that the strait was roughly 60 miles across, and that would appear to be accurate when taking a gander at the map.
So, next we calculate the area of the fleets. This is where a lot of assuming takes place. On average, we said that most of the ships are roughly the size of a Carrack, i.e. 25 metres in length. The length of the mast is what interested us more, because it appears in the photo below that the spacing between each ship is around two masts' worth.
View attachment 85349
So, let's say that each of these masts is around 40 metres tall. That'd mean that each ship needs around 80 metres around it, which is great because now we have a circle. To calculate the size of the fleet we simply have to figure out how big is a circle made up of 1000 circles. Then of 2500 circles.
Warwolf did the maths so if something's wrong it's his fault. Anyway,
he calculated that the Greyjoy fleet would be roughly 1.57 miles in size if the fleet was circular, which it appears to be. Danny's fleet would be around 2.5 miles. Add those two up, and the overall size of both fleets is 4.7 miles. BUT WAIT THERE IS MORE. You have to recognise the importance of the line of horizon, and how far a human being can see. At a height of 30 metres, the distance to the horizon is 12.2 miles. Even if we assume that 40 metres make it go up to 13 miles, which we did, that still means that the maximum distance from which the two fleets can spot each other is 17.7 miles. Remember that the strait is about 60 miles wide. So there you have it. Again, this isn't an exact science.